Abstract
We study inflationary solution in an extension of mimetic gravity with the higher derivative interactions coupled to gravity. Because of the higher derivative interactions the setup is free from the ghost and gradient instabilities while it hosts a number of novel properties. The dispersion relation of scalar perturbations develop quartic momentum correction similar to the setup of ghost inflation. Furthermore, the tilt of tensor perturbations can take either signs with a modified consistency relation between the tilt and the amplitude of tensor perturbations. Despite the presence of higher derivative interactions coupled to gravity the tensor perturbations propagate with the speed equal to the speed of light as required by the LIGO observations. Furthermore, the higher derivative interactions induce non-trivial interactions in cubic Hamiltonian, generating non-Gaussianities in various shapes such as the equilateral, orthogonal and squeezed configurations with observable amplitudes.
Highlights
We study inflationary solution in an extension of mimetic gravity with the higher derivative interactions coupled to gravity
The original version of the mimetic theory is free from instabilities [38, 39], but there is no nontrivial dynamics for scalar-type fluctuations
In this paper we have studied inflationary solution in an extension of mimetic gravity with higher derivative interactions coupled to gravity
Summary
We study the background dynamics to obtain a period of inflation in early universe. We have allowed a potential term for the mimetic field which will drive inflation In this setup P and F are arbitrary smooth function of χ. While the functions P (χ) and F (χ) are arbitrary, but in order to obtain a dark matter candidate in this setup one requires the combination K defined in eq (2.9) to be a constant. To obtain an inflationary solution in this setup we need a negative potential This should be compared with the analysis in [4] where F. In order to achieve reheating one has to modify the current setup and couple the mimetic field to the SM fields one way or another This is an open question which deserves a separate study elsewhere. We comment that in the current setup with the potential (2.14) a dark matter solution is inherited in the solution for t > 0 so one may only need reheating to generate the host radiation while the dark matter can come from the mimetic source
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